In a large dish or zip-top bag, combine lemon juice, zest, olive oil, garlic, oregano, cumin, pepper, and salt. Add lamb cubes and coat well with marinade. Refrigerate 2-4 hours.
When ready to cook, drain excess marinade and thread lamb onto skewers.
Preheat bbq grill or heavy-based pan to high. Cook lamb skewers for 5-6 minutes, turning to sear all sides. Transfer to a serving platter, cover with foil, and rest 5 minutes.
Combine parsley, cucumber, tomatoes, olives, oil, and vinegar in a bowl. Season to taste with salt and pepper. Serve lamb souvlaki with salad, wraps, pickled onion, and tzatziki.